Exercise 1: [5 points] Constrained Optimization Consider the following constrained optimization problem min xi + 2x2 + x2 +0.52 22 (1) s.t. max{|x1|, |X2|} = 2. (2) a) [1 point] Is this optimization problem convex? b) [1 point] Give the Lagrangian function L associated with this optimization problem. c) [2 points] Determine the Karush-KuhnTucker (KKT) conditions and find the points that satisfy these conditions. d) [1 point] Find the optimal solution. Exercise 1: [5 points] Constrained Optimization Consider the following constrained optimization problem min xi + 2x2 + x2 +0.52 22 (1) s.t. max{|x1|, |X2|} = 2. (2) a) [1 point] Is this optimization problem convex? b) [1 point] Give the Lagrangian function L associated with this optimization problem. c) [2 points] Determine the Karush-KuhnTucker (KKT) conditions and find the points that satisfy these conditions. d) [1 point] Find the optimal solution